13 CPMS Biomechanics Tissue Mechanics I 2024.pdf

Biomechanics & Surgery: Tissue Mechanics I At the completion of this lecture, the student will be able to: Familiarize the students with basic definitions of tissue mechanics and materials terms Describe some of the most useful and general properties of tissue Provide an appreciation of the clinical...

Biomechanics & Surgery: Tissue Mechanics I At the completion of this lecture, the student will be able to: Familiarize the students with basic definitions of tissue mechanics and materials terms Describe some of the most useful and general properties of tissue Provide an appreciation of the clinical relevance of mechanical properties of biological tissues Vassilios G. Vardaxis, Ph.D. Tissue Mechanics n How does tissue respond to loading? – When does it fail? – With what type of loading is it weakest? strongest? n How extensible are the various tissues? – What effect does stiffness have on injury? n How does the tissue’s structure influence its function? – Does tissue geometry influence its strength? – What, if any, advantage does composite tissue offer? Vassilios G. Vardaxis, Ph.D. Application Injury occurs when an imposed load exceeds the tolerance (load-carrying ability) of a tissue n – Training effects Hippocrates (460-377 B.C.) “All parts of the body which have a function, if used in moderation and exercises in labours to which each are accustomed, thereby become healthy and well-developed: but if unused and left idle, they become liable to disease, defective in growth, and age quickly. This is especially the case with joints and ligaments, if one doe not use them.” LeVay 1990. p30 – Equipment Design effects Vassilios G. Vardaxis, Ph.D. Structural vs. Material Properties Vassilios G. Vardaxis, Ph.D. Stress A force tries to rearrange the molecules in an object: Øit may push them closer together (compressive stress); Øit may pull them further apart (tensile stress); Øit may slide one layer across another (shear stress). n Stress (s): internal resistance to an external load Axial Shear – Axial (compressive or tensile) s=F/A – Shear t = F/A (parallel or tangential forces) n Units Pascal (Pa) = 1N/m2 Vassilios G. Vardaxis, Ph.D. Strain n n Change in shape or deformation (e) strain – DL/Lo – Ddimension / original dimension The three types of strain correspond to the three types of stress: Ø pushing together of the molecules (compressive strain); Ø separation of the molecules (tensile strain); Ø sliding of molecules layer on layer (shear strain). Strain is measured as a proportional change in dimension. Strain is a ratio - it has no actual units. Vassilios G. Vardaxis, Ph.D. How are Stress (σ) and Strain (ε) related? “Stress is what is done to an object, strain is how the object responds”. Stress and Strain are proportional to each other. Vassilios G. Vardaxis, Ph.D. Stress & Strain n Stress-strain ratio: stiffness or compliance of the material – E = s/ e Young’s Modulus n A s Linear material B – Hooke’ law: s = E * e n Biological material non-linear due to its tissue fluid component (viscoelastic properties) e Vassilios G. Vardaxis, Ph.D. Elastic region & Plastic region Vassilios G. Vardaxis, Ph.D. Stiffness (Elastic Modulus) Stiffness (Elastic Modulus, Young’s modulus, modulus of elasticity) Hooke’s law (posits that stress and strain are linearly related – only true for biological tissues when the magnitude of the stretch is relatively small Linear response at low loads Vassilios G. Vardaxis, Ph.D. Yield Point Vassilios G. Vardaxis, Ph.D. Extensibility Vassilios G. Vardaxis, Ph.D. Bending n n n n n Long bones: beams Compressive stress: inner portion Tensile stress: outer portion Max stresses near the edges Less near the neutral axis Vassilios G. Vardaxis, Ph.D. Bending n Three-point bending – failure at middle – ski boot fracture n Four-point bending – failure at the weakest point between two inside forces Vassilios G. Vardaxis, Ph.D. Bending n n Cantilever bending Compressive force acting off-center from long axis Vassilios G. Vardaxis, Ph.D. Bending Summary If a moment is applied to an object (e.g. a force is applied eccentrically), it will produce bending. The amount of bending depends on the magnitude of this "bending moment" and on the shape and mechanical properties of the object being bent. When an object bends: Ø one side becomes concave - this side is in compression; Ø the other side becomes convex - this side is in tension; Ø between the two sides is an unstressed "neutral axis"; Ø the highest tensile and compressive stresses are on the outer surfaces; Ø the whole of the bent area is subject to shear stress. Vassilios G. Vardaxis, Ph.D. Torsion n n Twisting action applied to a structure Larger radius of the shaft, greater resistance ro ri n n Stiffer the material harder to deform In addition to shear stress, normal stress (tensile & compressive) are produced in a helical path (spiral fractures) r Vassilios G. Vardaxis, Ph.D. Brittleness - Absence of any plastic deformation prior to failure Resilience - measure of energy absorbed by a material and returned when load is removed; materials that quickly return to their original shape are called resilient 1 2 3 Toughness – property of a material enabling it to endure high-impact or shock loads; ability to absorb energy during plastic deformation; measure of the capacity of a material to sustain permanent deformation Vassilios G. Vardaxis, Ph.D. Uniqueness of Biological Materials Anisotropic Viscoelastic Time-dependent behavior Loading rate-dependent behavior Organic Self-repair Adaptation to changes in mechanical demand Vassilios G. Vardaxis, Ph.D. n Provided by the fluid component in biological tissue n Resistance to flow n Affects stress-strain n Viscoelasticity Increase in strain rate produces –increase in stiffness of the material Vassilios G. Vardaxis, Ph.D. Viscoelasticity n Pure elastic material – Not viscoelastic – All energy returned – No energy loss n Hysteresis: area representing energy lost lo a d Viscoelastic un – lose energy due to heat – energy is not returned immediately s ad Viscoelastic tissues Lo n Elastic e Vassilios G. Vardaxis, Ph.D. Hysteresis loading and unloading path is different resulting in a loss of energy lost energy ad in g ng lo lo i ad un stress (s) recovered energy strain (e) Vassilios G. Vardaxis, Ph.D. Viscoelasticity Displacement is a function of time deformation creep initial length loaded length loaded length over time load time Vassilios G. Vardaxis, Ph.D. Vassilios G. Vardaxis, Ph.D. Vassilios G. Vardaxis, Ph.D. Viscoelasticity n Stresses and strains are dependent on: – time – rate of loading General rules: n The longer it takes for a load to be applied: – strain ­ – stress ¯ n The faster it takes for a load to be applied: – strain ¯ – stress ­ Vassilios G. Vardaxis, Ph.D. Viscoelasticity - Summary A material which is "viscoelastic" shows elastic behavior, but is slow to recover, and returns less energy. The stress/strain curve of a viscoelastic material shows hysteresis, which is dependent on the rate of applying and removing strain. Viscoelastic materials are stiffer at higher strain rates. Viscoelastic materials "creep", which means they continue to deform while stress is kept applied. Cartilage shows marked creep, as fluid is expelled with continued loading. Polymers, such as polyethylene, also show creep. Vassilios G. Vardaxis, Ph.D. Material Fatigue & Failure First/early cycles effect: shift in mechanical response n Cumulative effect: Continued loading failure Fatigue: repeated loads above a certain threshold Initial cycles effect n 1 2 3 n s e Vassilios G. Vardaxis, Ph.D. Material Failure Summary All materials will break if the strain is high enough. However, materials differ in what happens first. Ø If a material completely recovers from strain, it shows "elastic" deformation. Ø If a material shows permanent deformation following strain, it shows "plastic" deformation. Most materials are elastic at low strains. At higher strains: Ø a "brittle" material will continue to deform elastically until it breaks; Ø a "malleable" or "ductile" material will deform plastically before it breaks. The stress at which a material's deformation changes from elastic to plastic is known as the "yield stress" or "elastic limit". The "toughness" of a material is the amount of energy it can absorb before it breaks. Vassilios G. Vardaxis, Ph.D.